On the Importance of Shear Deformation, Rotatory Inertia, and Coriolis Forces in Turbine Blade Vibrations

Abstract

This paper is concerned with the significance of the effects of shear deformation, rotatory inertia, and Coriolis forces in the analysis of turbine blade vibrations. Since these are quite pronounced at the high frequency ranges encountered in turbine blade vibration problems, they should not be overlooked although their inclusion paves the way for a complicated nonlinear analysis. An approximate analysis technique is presented which involves an application of the stationary functional method using the normal modes of a discretized model. Numerical results for a typical blade are obtained and discussed. An advantage of this analysis as applied to a lumped parameter model is that nonlinear modes higher than the fundamental can also be easily computed and assessed.

Identifying the significance of nonlinear normal modes

“…where the coordinates of the system pass through the equilibrium and reach their extrema simultaneously. Numerous theoretical studies followed this original work [5][6][7][8], and NNMs were established as a valuable tool for investigating the behaviour of a variety of nonlinear systems [9,10]. Importantly, it was shown that NNMs (describing the dynamics of the underlying conservative system) could be used to gain an understanding of the resonant forced responses of the system [11].…”

The efficient inclusion of rotation-induced inertia effects in a shaft-blisk assembly model using zero-speed modes

“…This section describes how the translational deflections of the mode shape are used to obtain the corresponding angular deformation data required for the matrices of Eqs. ( 22) and (27).…”

“…The trend towards increased efficiency at higher speeds has led to larger blades and stronger stagger angles, which generate large centrifugal and Coriolis forces [26]. Some early studies ignored the Coriolis effects since they were limited to small motions or to beams that are rigid in bending except at disk connection [27]. Krupka and Baumanis [28] found that both shear deformation and rotary inertia should be included in the analysis, as they result in changes of about 4% to 8% in first and second natural frequencies at high speeds.…”

The coupled vibration in a shaft‐disk‐blades system

“…The vibration characteristics of blades at a constant rotating speed have been studied by many investigators, e.g., Lintins et al (1973), Bauer (1980), Subrahmanyam et al (1982), Sisto et al (1983), Subrahmanyam and Kaza (1986), Ansari (1986), Bauer and Eidel (1988), Kammer and Schlack (1987a;1987b), Yigit et al (1988), Huang and Lin (1990) and Chiou and Yeh (1991). The blades were assumed as a rotating beam, uniform or pretwisted.…”